x^2-18x+23.24=

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Solution for x^2-18x+23.24= equation:


Simplifying
x2 + -18x + 23.24 = 0

Reorder the terms:
23.24 + -18x + x2 = 0

Solving
23.24 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-23.24' to each side of the equation.
23.24 + -18x + -23.24 + x2 = 0 + -23.24

Reorder the terms:
23.24 + -23.24 + -18x + x2 = 0 + -23.24

Combine like terms: 23.24 + -23.24 = 0.00
0.00 + -18x + x2 = 0 + -23.24
-18x + x2 = 0 + -23.24

Combine like terms: 0 + -23.24 = -23.24
-18x + x2 = -23.24

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -23.24 + 81

Reorder the terms:
81 + -18x + x2 = -23.24 + 81

Combine like terms: -23.24 + 81 = 57.76
81 + -18x + x2 = 57.76

Factor a perfect square on the left side:
(x + -9)(x + -9) = 57.76

Calculate the square root of the right side: 7.6

Break this problem into two subproblems by setting 
(x + -9) equal to 7.6 and -7.6.

Subproblem 1

x + -9 = 7.6 Simplifying x + -9 = 7.6 Reorder the terms: -9 + x = 7.6 Solving -9 + x = 7.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 7.6 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.6 + 9 x = 7.6 + 9 Combine like terms: 7.6 + 9 = 16.6 x = 16.6 Simplifying x = 16.6

Subproblem 2

x + -9 = -7.6 Simplifying x + -9 = -7.6 Reorder the terms: -9 + x = -7.6 Solving -9 + x = -7.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -7.6 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.6 + 9 x = -7.6 + 9 Combine like terms: -7.6 + 9 = 1.4 x = 1.4 Simplifying x = 1.4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.6, 1.4}

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